This must be a seriously stupid question for people well versed in Dimensions and Hierarchies so I hope to get a quick answer.

I have a simple Dimension called DimTagInstance which has 3 Attributes (Id, Site Id, Latitude, Longitude). I would like to be able to access the Value of the other Attributes when I am in the context of another one.

I have written the following query but it returns All for the Value.

WITH MEMBER Measures.Latitude AS [DimTagInstance].[Latitude].CURRENTMEMBER.Name

It will show "All" because in your query you are specifying a different member.

So in the context of [DimTagInstance].[Site Id].[Site Id] the calculation [DimTagInstance].[Latitude].CURRENTMEMBER.Name will return "All" because you are not including the [DimTagInstance].[Latitude] members in the query. If you did something like

WITH MEMBERMeasures.Latitude AS[DimTagInstance].[Latitude].CURRENTMEMBER.Name